Nonlinear Approximation Theory

摘要: The first investigations of nonlinear approximation problems were made by P.L. Chebyshev in the last century, and entire theory uniform approxima tion is strongly connected with his name. By making use ideas, theories best rational functions polynomials developed over years an almost unified framework. difference between linear its implications became apparent 1960's. At roughly same time other approaches to also developed. new tools, such as functional analysis topological methods, showed that linearization not sufficient for a complete treatment families. In particular, application global consideration flows on family approximating intro duced ideas which previously unknown theory. These still are important many branches analysis. On hand, methods prob lems can often be successfully applied belong or arise from approximation. An example solution moment via Best quadrature formulae search spaces leads spline free nodes. most famous problem this kind, namely interpolation poly nomials, treated appendix book."